KANSAS CITY, Mo. — New York has a new closer who seems to thrive in the playoffs, but even when Mariano Rivera was dominating Octobers late in his career, Jeurys Familia wasn’t paying all that much attention.

And for good reason.

It wasn’t until late in the 2012 season that Familia began the transition from being a starting pitcher to a reliever.

“That was something I never thought about doing,” Familia said.

So he never really watched the Yankees closer in the postseason, since Rivera missed the 2012 playoffs with a knee injury and then ended his career in the regular season when the Yankees missed the playoffs a year later.

Still, Familia appreciates how important it is to be the closer this time of year and uses Rivera as something of the ultimate example.

“Everybody knows he’s the best in the game, one of the best closers ever in the major leagues,” Familia said Monday at Kauffman Stadium before the Mets’ workout. “For me, every time I’ve got the opportunity to close a game or be in a game, I treat it the same way.”

Through the first two rounds, that attitude has served Familia and the Mets well.

He’s pitched in eight games and hasn’t given up a run in 9 ²/₃ innings against the Dodgers and Cubs, earning five saves along the way — while giving up just two hits and a pair of walks.

Despite his relative lack of experience, he’s already emerged as the most dependable part of the Mets otherwise shaky bullpen.

“I don’t care if it’s the postseason or the World Series, I think back to it’s the same game I played in the Dominican, the same game I played in the minor leagues,” Familia said. “I just go out there, enjoy the moment and do the best I can.”

And he’s tried to embrace his current role.

“This has been unbelievable,” Familia said. “I love being in at end of game. Right now, baseball is everything to me.”